def test_ground_state_matches(self, dense, MPO_ham, cyclic):
n = 10
tol = 3e-2 if cyclic else 1e-4
h = MPO_ham(n, cyclic=cyclic)
dmrg = DMRG1(h, bond_dims=[4, 8, 12])
dmrg.opts['local_eig_ham_dense'] = dense
dmrg.opts['periodic_segment_size'] = 1.0
dmrg.opts['periodic_nullspace_fudge_factor'] = 1e-6
assert dmrg.solve(tol=tol / 10, verbosity=1)
assert dmrg.state.cyclic == cyclic
eff_e, mps_gs = dmrg.energy, dmrg.state
mps_gs_dense = mps_gs.to_dense()
assert_allclose(mps_gs_dense.H @ mps_gs_dense, 1.0, rtol=tol)
h_dense = h.to_dense()
# check against dense form
actual_e, gs = eigh(h_dense, k=1)
assert_allclose(actual_e, eff_e, rtol=tol)
assert_allclose(abs(expec(mps_gs_dense, gs)), 1.0, rtol=tol)
# check against actual MPO_ham
if MPO_ham is MPO_ham_XY:
ham_dense = ham_heis(n, cyclic=cyclic,
j=(1.0, 1.0, 0.0), sparse=True)
elif MPO_ham is MPO_ham_heis:
ham_dense = ham_heis(n, cyclic=cyclic, sparse=True)
actual_e, gs = eigh(ham_dense, k=1)
assert_allclose(actual_e, eff_e, rtol=tol)
assert_allclose(abs(expec(mps_gs_dense, gs)), 1.0, rtol=tol)
def test_ground_state_matches(self, dense, MPO_ham):
h = MPO_ham(6)
dmrg = DMRG1(h, bond_dims=8)
dmrg.opts['eff_eig_dense'] = dense
assert dmrg.solve()
eff_e, mps_gs = dmrg.energy, dmrg.state
mps_gs_dense = mps_gs.to_dense()
assert_allclose(mps_gs_dense.H @ mps_gs_dense, 1.0)
h_dense = h.to_dense()
# check against dense form
actual_e, gs = seigsys(h_dense, k=1)
assert_allclose(actual_e, eff_e)
assert_allclose(abs(expec(mps_gs_dense, gs)), 1.0)
# check against actual MPO_ham
if MPO_ham is MPO_ham_XY:
ham_dense = ham_heis(6, cyclic=False, j=(1.0, 1.0, 0.0))
elif MPO_ham is MPO_ham_heis:
ham_dense = ham_heis(6, cyclic=False)
actual_e, gs = seigsys(ham_dense, k=1)
assert_allclose(actual_e, eff_e)
assert_allclose(abs(expec(mps_gs_dense, gs)), 1.0)
def test_ising_and_MPS_product_state(self):
h = MPO_ham_ising(6, bx=2.0, j=0.1)
dmrg = DMRG1(h, bond_dims=8)
assert dmrg.solve(verbosity=1)
eff_e, mps_gs = dmrg.energy, dmrg.state
mps_gs_dense = mps_gs.to_dense()
assert_allclose(mps_gs_dense.H @ mps_gs_dense, 1.0)
# check against dense
h_dense = h.to_dense()
actual_e, gs = eigh(h_dense, k=1)
assert_allclose(actual_e, eff_e)
assert_allclose(abs(expec(mps_gs_dense, gs)), 1.0)
exp_gs = MPS_product_state([plus()] * 6)
assert_allclose(abs(exp_gs.H @ mps_gs), 1.0, rtol=1e-3)
def test_single_explicit_sweep(self):
h = MPO_ham_heis(5)
dmrg = DMRG1(h, bond_dims=3)
assert dmrg._k[0].dtype == float
energy_tn = (dmrg._b | dmrg.ham | dmrg._k)
e0 = energy_tn ^ ...
assert abs(e0.imag) < 1e-13
de1 = dmrg.sweep_right()
e1 = energy_tn ^ ...
assert_allclose(de1, e1)
assert abs(e1.imag) < 1e-13
de2 = dmrg.sweep_right()
e2 = energy_tn ^ ...
assert_allclose(de2, e2)
assert abs(e2.imag) < 1e-13
# state is already left canonized after right sweep
de3 = dmrg.sweep_left(canonize=False)
e3 = energy_tn ^ ...
assert_allclose(de3, e3)
assert abs(e2.imag) < 1e-13
de4 = dmrg.sweep_left()
e4 = energy_tn ^ ...
assert_allclose(de4, e4)
assert abs(e2.imag) < 1e-13
# test still normalized
assert dmrg._k[0].dtype == float
align_TN_1D(dmrg._k, dmrg._b, inplace=True)
assert_allclose(abs(dmrg._b @ dmrg._k), 1)
assert e1.real < e0.real
assert e2.real < e1.real
assert e3.real < e2.real
assert e4.real < e3.real